Matrix-Based Multigrid - Yair Shapira

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Résumé :
This book introduces and analyzes the multigrid approach for the numerical solution of large sparse linear systems arising from the discretization of elliptic partial differential equations. Special attention is given to the powerful matrix-based-multigrid approach, which is particularly useful for problems with variable coefficients and nonsymmetric and indefinite problems. This approach applies not only to model problems on rectangular grids but also to more realistic applications with complicated grids and domains and discontinuous coefficients. This second edition offers improved content and provides more explanation for the non-expert....

Biographie:
Yair Shapira, PhD, Department of Computer Science, Technion, Israeli Institute of Technology...

Sommaire:
List of Figures List of Tables Preface Part I. Concepts and Preliminaries 1. The Multilevel?Multiscale Approach 2. Preliminaries Part II. Partial Differential Equations and Their Discretization 3. Finite Differences and Volumes 4. Finite Elements Part III. Numerical Solution of Large Sparse Linear Systems 5. Iterative Linear System Solvers 6. The Multigrid Iteration Part IV. Multigrid for Structured Grids 7. Automatic Multigrid 8. Applications in Image Processing 9. Black-Box Multigrid 10. The Indefinite Helmholtz Equation 11. Matrix-Based Semicoarsening Part V. Multigrid for Semi-Structured Grids 12. Multigrid for Locally Refined Meshes 13. Application to Semi-Structured Grids Part VI. Multigrid for Unstructured Grids 14. Domain Decomposition 15. The Algebraic Multilevel Method 16. Applications 17. Semialgebraic Multilevel for Systems of PDEs Part VII. Appendices 18. Time-Dependent Parabolic PDEs 19. Nonlinear Equations References Index